Page 89 - 48Fundamentals of Compressible Fluid Mechanics

4.2. ISENTROPIC CONVERGING-DIVERGING FLOW IN CROSS SECTION 51

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4.2.3 Mass Flow Rate (Number) (

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3 3'3
( 3 /( %((

3*
3

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One of the important engineering parameters is the mass flow rate which is at any
point is
(4.45)

This parameter is studied here, to examine the maximum flow rate and to see what

is the effect of the compressibility on the flow rate. The area ratio as a function of
the Mach number needed to be established, specifically and explicitly the relation-
ship for the chocked flow. The area ratio is defined as the ratio of the cross section
at any point to the throat area (the narrow area). It is convenient to rearrange the
equation (4.45) to be expressed in terms of the stagnation properties as
(4.46)

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Expressing the temperature in term of Mach number in equation (4.46) results in

, ,
, ,

(4.47)

It can be noted that equation (4.47) holds everywhere in the converging-diverging

duct and this statement also true for the throat. The throat area can be denoted

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as by . It can be noticed that at the throat when the flow is chocked or in other
words
and that the stagnation conditions (i.e. temperature, pressure) do
not change. Hence equation (4.47) obtained the form

(4.48)

Since the mass flow rate is constant in the duct, dividing equations (4.48) by

equation (4.47) yields
"

(4.49)

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